Related papers: Metric Distortion in Peer Selection
In distortion-based analysis of social choice rules over metric spaces, one assumes that all voters and candidates are jointly embedded in a common metric space. Voters rank candidates by non-decreasing distance. The mechanism, receiving…
Distortion-based analysis has established itself as a fruitful framework for comparing voting mechanisms. m voters and n candidates are jointly embedded in an (unknown) metric space, and the voters submit rankings of candidates by…
We consider committee election of $k \geq 2$ (out of $m \geq k+1$) candidates, where the voters and the candidates are associated with locations on the real line. Each voter's cardinal preferences over candidates correspond to her distance…
We consider a voting problem in which a set of agents have metric preferences over a set of alternatives, and are also partitioned into disjoint groups. Given information about the preferences of the agents and their groups, our goal is to…
Social choice theory offers a wealth of approaches for selecting a candidate on behalf of voters based on their reported preference rankings over options. When voters have underlying utilities for these options, however, using preference…
We consider the matching problem in the metric distortion framework. There are $n$ agents and $n$ items occupying points in a shared metric space, and the goal is to design a matching mechanism that outputs a low-cost matching between the…
We consider the distributed single-winner metric voting problem on a line, where agents and alternative are represented by points on the line of real numbers, the agents are partitioned into disjoint districts, and the goal is to choose a…
We study single-candidate voting embedded in a metric space, where both voters and candidates are points in the space, and the distances between voters and candidates specify the voters' preferences over candidates. In the voting, each…
A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is…
We consider a distributed voting problem with a set of agents that are partitioned into disjoint groups and a set of obnoxious alternatives. Agents and alternatives are represented by points in a metric space. The goal is to compute the…
We study the design of voting rules in the metric distortion framework. It is known that any deterministic rule suffers distortion of at least $3$, and that randomized rules can achieve distortion strictly less than $3$, often at the cost…
We develop new voting mechanisms for the case when voters and candidates are located in an arbitrary unknown metric space, and the goal is to choose a candidate minimizing social cost: the total distance from the voters to this candidate.…
We determine the quality of randomized social choice mechanisms in a setting in which the agents have metric preferences: every agent has a cost for each alternative, and these costs form a metric. We assume that these costs are unknown to…
We study higher statistical moments of Distortion for randomized social choice in a metric implicit utilitarian model. The Distortion of a social choice mechanism is the expected approximation factor with respect to the optimal utilitarian…
The metric distortion of a randomized social choice function (RSCF) quantifies its worst-case approximation ratio to the optimal social cost when the voters' costs for alternatives are given by distances in a metric space. This notion has…
A voting rule decides on a probability distribution over a set of m alternatives, based on rankings of those alternatives provided by agents. We assume that agents have cardinal utility functions over the alternatives, but voting rules have…
In light of the classic impossibility results of Arrow and Gibbard and Satterthwaite regarding voting with ordinal rules, there has been recent interest in characterizing how well common voting rules approximate the social optimum. In order…
We revisit the recent breakthrough result of Gkatzelis et al. on (single-winner) metric voting, which showed that the optimal distortion of 3 can be achieved by a mechanism called Plurality Matching. The rule picks an arbitrary candidate…
We study the distortion of one-sided and two-sided matching problems on the line. In the one-sided case, $n$ agents need to be matched to $n$ items, and each agent's cost in a matching is their distance from the item they were matched to.…
In this note, we uncover three connections between the metric distortion problem and voting methods and axioms from the social choice literature.